# How do you solve the equation 2(x+2)^2=72?

Mar 22, 2017

"answer "{x=-8" , "x=4}

#### Explanation:

$2 {\left(x + 2\right)}^{2} = 72$

$\text{divide both sides by 2}$

$\frac{\cancel{2} {\left(x + 2\right)}^{2}}{\cancel{2}} = \frac{72}{2}$

${\left(x + 2\right)}^{2} = 36$

$\text{take square root both sides}$

$\left(x + 2\right) = \pm 6$

$\text{if "x+2=-6" , then } x = - 8$

$\text{if "x+2=6 " , then } x = 4$

Mar 22, 2017

$x = 4$ or $- 8$

#### Explanation:

$2 {\left(x + 2\right)}^{2} = 72$

divide by $2$:

${\left(x + 2\right)}^{2} = 36$

square root:

$x + 2 = 6$ or $- 6$

subtract $2$:

$x = 4$ or $- 8$

Mar 22, 2017

$x = \left\{4 , - 8\right\}$

#### Explanation:

First divide both sides by two to get ${\left(x + 2\right)}^{2} = 36$. Next take the square root of both sides to get $x + 2 = \pm 6$. Now split this into two equations for both the positive and negative six. These look like: $x + 2 = 6$ and $x + 2 = - 6$. For both equations, subtract two from both sides which gives you $x = 4$ and $x = - 8$. Hence $x = \left\{4 , - 8\right\}$.

Mar 22, 2017

$x = - 8 \text{ or } x = 4$

#### Explanation:

Divide both sides by 2

$\Rightarrow \frac{2}{2} {\left(x + 2\right)}^{2} = \frac{72}{2}$

$\Rightarrow {\left(x + 2\right)}^{2} = 36$

Take the $\textcolor{b l u e}{\text{square root of both sides}}$

$\sqrt{{\left(x + 2\right)}^{2}} = \textcolor{red}{\pm} \sqrt{36}$

$\Rightarrow x + 2 = \textcolor{red}{\pm} 6$

• x+2=color(red)(6)

subtract 2 from both sides.

$x \cancel{+ 2} \cancel{- 2} = 6 - 2$

$\Rightarrow x = 4$

• x+2=color(red)(-6)

$\Rightarrow x = - 8$

$\textcolor{b l u e}{\text{as a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$x = 4 \to 2 {\left(4 + 2\right)}^{2} = 2 \times 36 = 72 \to \text{ true}$

$x = - 8 \to 2 {\left(- 8 + 2\right)}^{2} = 2 \times 36 = 72 \to \text{ true}$

$\Rightarrow x = - 8 \text{ or " x=4" are the solutions}$